1. This assignment is important in providing feedback and helping to establish competency in essential skills.
2. Answer all the questions. The questions are not of equal weight, and some questions are worth much more than others.
3. The questions relate to material up to and including Module 8.
4. Read the Notes Concerning Assignments (page 15) before starting this Assignment.
5. When you are asked to comment on a ¯nding, usually a short paragraph is all that is required.
6. For all graphs, label the axes correctly, include a contextual title and the units of measurement.
7. In many cases, spss output contains much more information than is required for a correct and complete answer. In those cases just reproducing the output may not attract any marks. Make sure you report only the information from the spss output relevant to your answer.
Question 1
The average heart rate of adults is usually no more than ninety beats per minute. In a study to identify risk factors associated with cardiac arrest, measurements of heart rate were taken for each of the 70 critically ill patients who survived cardiac arrest. The data are available in the file shock.sav.
(a) Using spss, compute an estimate of the mean and standard deviation of heart rate for all critically ill patients who survived cardiac arrest after being admitted to hospital. HINT - Select only those patients who survived for this question.
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(b) Obtain a 98% con¯dence interval for the true mean heart rate for all critically ill patients admitted to hospital in cardiac arrest who survived.
(c) Justify the use of the con¯dence interval formula in part (b) by checking the appropriate conditions and assumptions (include an appropriate graph to support your answer).
(d) Perform a hypothesis test to see if the mean heart rate for critically ill patients admitted to hospital in cardiac arrest who survived is higher than the overall population. In performing this test, include:
(i) Both hypotheses, clearly de¯ning all symbols.
(ii) State and justify any assumptions.
(iii) Calculate the test statistic.
(iv) Calculate the p-value.
(v) A meaningful conclusion.
Question 2
Researchers at the Shock Research Unit (you do NOT need to use the data set for this question) have records to indicate that the mean age of patients who enter hospital with cardiac arrest follows an approximately normal distribution with mean of 50 years and a standard deviation of 15 years.
(a) Use this information to estimate the percentage of patients who are 45 years or younger.
(b) One group of 50 cardiac arrest patients' have a mean age of 45. One researcher at the Shock unit claims that this is not an unusual occurrence, a second researcher claims that it is. Using this information calculate the following to show which researcher is correct:
(i) Describe the shape, centre and spread of the distribution of mean ages for the sample of 50 cardiac arrest patients.
(ii) Assuming that this group of 50 patients represent a random sample of all cardiac arrest patients, calculate the probability that the mean age is 45 years or younger. In doing so, state which researcher is correct.
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Question 3
Does it take less time for the blood to pump around the body for those who survive cardiac arrest compared with those who ultimately do not survive? (Use the information in the shock.sav data to answer the following questions).
(a) Using spss, compute the mean and standard deviation of circulation time for those who survived and those who do not survive cardiac arrest.
(b) Perform a hypothesis test to see if mean circulation time for those who survive cardiac arrest is lower than the mean circulation time for those who do not survive cardiac arrest. In performing this test, include:
(i) Both hypotheses, clearly defining all symbols.
(ii) State and justify any assumptions.
(iii) Calculate the test statistic.
(iv) Calculate the p-value.
(v) A meaningful conclusion.
(c) Without using spss, compute a 95% con¯dence interval for the di®erence in the mean circulation time for those who survive cardiac arrest and those who do not survive cardiac arrest. (You can use the results from spss computed in the previous parts of this question, but you must do the calculations for the actual confidence interval without using spss.)
Question 4
In a random sample of 320 Data Analysis students, 190 claimed to thoroughly enjoy studying statistics.
(a) Estimate, with 90% con¯dence, the true population proportion of Data Analysis students who thoroughly enjoy studying statistics.
(b) Check the procedure you used in part (a) is appropriate by checking all the necessary conditions and assumptions.
(c) What sample size is required if we wish to population proportion of Data Analysis students who thoroughly enjoy studying statistics, to within plus or minus 2%, with 99% confidence? Use a conservative method in determining the sample size.
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Question 5
Evidence suggests that non-smokers who live with smokers and are therefore exposed to sidestream smoke (as opposed to mainstream smoke, which is inhaled by the smoker directly from the cigarette) may have increased risk of lung disease. Mainstream and sidestream yields (in mg) of tar, nicotine, and carbon monoxide for eight nonfilter cigarettes appeared in the paper \Yields of Tar, Nicotine, and Carbon Monoxide in Sidestream Smoke of Canadian Cigarettes" (Amer. J. Public Health (1984):228{231).
Data on tar yield is given below.
Cigarette Sidestream Mainstream
Yield Yield
1 15.8 18.5
2 16.9 17.0
3 21.6 17.2
4 18.8 19.4
5 29.3 15.6
6 20.7 16.4
7 18.9 13.3
8 25.0 10.2
Is there evidence that non-smokers who live with smokers have an increased risk of lung disease? In other words, is the mean yield (in mg) of tar, nicotine, and carbon monoxide greater in sidestream smoke than in mainstream smoke?
(a) Use a parametric test (a t-test) to answer this health concern. In performing this test, include:
(i) Both hypotheses, clearly defining all symbols.
(ii) State and justify any assumptions.
(iii) Calculate the test statistic.
(iv) Calculate the p-value.
(v) Write a meaningful conclusion.
(b) Use a non-parametric test to answer this health concern. In performing this test, include:
(i) Both hypotheses, clearly defining all symbols.
(ii) Calculate the test statistic.
(iii) Calculate the p-value.
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(iv) Write a meaningful conclusion.
(c) Comment on any differences found between the two tests and why this may be the case.